I'm not sure what you mean by "the boot session," unless you meant "root session," because what you're trying to change is the password for root. If that's what you want, open a terminal and become root:
su -
and give the current root password when prompted. I'm suggesting "su -" instead of just su to get you fully logged in as root, with root's complete environment, just to be careful. Then, enter this:
passwd
When prompted, give the new password (It won't echo, so don't worry if nothing shows up in your terminal session.) and then, when asked, give it again. If and only if you've typed it exactly the same way both times, you'll be told that your password has been changed.
In case anybody reading this thinks that I'm giving information that could help an attacker gain control of a system, I'd like to point out that the only way to do this is to know the current root password and if an attacker already knows that, there's no need for this. Changing the root password if you've forgotten it is an entirely different kettle of fish that I'm not about to discuss in public.
